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Homogenization and Asymptotics for Small Transaction Costs

Author

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  • Halil Mete Soner

    (ETH Zürich, Ecole Polytechnique Fédérale de Lausanne, and Swiss Finance Institute)

  • Nizar Touzi

    (Ecole Polytechnique, Paris)

Abstract

We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic control problem which can be solved in closed form in the one-dimensional case. Unlike the existing literature, we consider a general utility function and general dynamics for the underlying assets. Our arguments are based on ideas from the homogenization theory and use the convergence tools from the theory of viscosity solutions. The multidimensional case is studied in our accompanying paper using the same approach.

Suggested Citation

  • Halil Mete Soner & Nizar Touzi, 2012. "Homogenization and Asymptotics for Small Transaction Costs," Swiss Finance Institute Research Paper Series 12-13, Swiss Finance Institute.
  • Handle: RePEc:chf:rpseri:rp1213
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    File URL: http://ssrn.com/abstract=2031571
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    Keywords

    transaction costs; homogenization; viscosity solutions; asymptotic expansions;
    All these keywords.

    JEL classification:

    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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